Homework Assignment #4: Propositional Logic. PHIL200_s12_hw_4

HOMEWORK ASSIGNMENT #4: PROPOSITIONAL LOGIC
Name:
Grade Course: PHIL 200:
Tutor’s Name:
(10 March 2012)
Homework Assignment #4: Propositional Logic
Part I
Instructions: Translate each of the following statements into symbolic form. Use the letters given in parentheses for the symbolization.
1. Your ice is not cold. (I)
I¬
2. My car does not look great, but it gets great gas mileage. (C, M)
C¬M
3. Either candy or tobacco is bad for your teeth. (C, T)
¬C ¬T
4. Toothpaste is good for your teeth, but tobacco is not. (T, B)
T ∧, ¬B
5. Driving too fast is hazardous to your health; also driving without buckling up. (F, B)
F∧, ¬B
6. Lava lamps are distracting while music in the background is soothing. (L, M)
L ∧, M ∧
7. Unless you stop eating too much pepperoni, you will develop a stomach ulcer. (S, U)
¬ S U ∧
8. Citizen Kane did not win the Academy Award for best picture, but it is still the greatest movie ever made. (C, G)
C ¬, G ∧
Part II
Instructions: For each of the following questions you are given a statement and truth-value assignment.
(A) translate the statement into symbolic form; (B) use the truth-value assignment to determine whether the statement is true or false.
9. My car is fast, if it has a turbocharger.
X = My car is fast.
Y = My car has a turbocharger.
Let X = False, Y = True.
Answer
a. X ∧, Y∧
b
X
Y
X ∧ Y
T
T
T
T
F
F
F
T
T
F
F
T
10. My car is not fast, unless it has a turbocharger.
X = My car is fast.
Y = My car has a turbocharger.
Let X = False, Y = False.
Answer
a. ¬X¬Y
b.
X
Y
¬X ¬ Y
T
T
T
T
F
F
F
T
F
F
F
F
Part III
Instructions: (A) Identify the main logical connective in each of the following symbolic statements. (B) Assuming P is true, Q is false, and R is true; determine the truth-value of each symbolic statement.
11. R & (¬P v Q) (and, not, or)
P =T, Q = F, and R = T
= T, F, & F
Statement is false
12. ~R (not)
P =T, Q = F, and R = T
= F (statement is false)
13. (P & ¬Q) v R (and, not, or)
T, T, and T (Statement is True)
14. R → ¬P then, not
P =T, Q = F, and R = T
T, → F (statement is false)
15. (P v (Q → R) & (¬R v P) (or, then, and...